4.1 Forces and Newton's laws of motion

Forces and Newton's laws are the backbone of sports biomechanics. They explain how athletes move, jump, throw, and interact with their environment. Understanding these concepts helps you optimize performance and prevent injuries across virtually every sport.

From the push-off in sprinting to the impact of a punch in boxing, forces shape every athletic movement. Newton's laws give you a framework for analyzing those forces, which is how coaches refine technique, engineers design better equipment, and athletes push the limits of what's possible.

Forces in Sports

Internal and External Forces

Every force acting on an athlete falls into one of two categories. Internal forces are generated by muscles, tendons, and ligaments within the body. These are what allow you to contract a muscle, swing a bat, or stabilize a joint. External forces come from the environment: gravity pulling you down, the ground pushing back up, air rushing past you, or an opponent making contact.

Athletic performance comes down to how well internal forces interact with external ones. A sprinter's leg muscles (internal) push against the ground, and the ground pushes back (external) to propel them forward. Neither force alone produces movement; it's the interaction that matters.

Gravitational and Normal Forces

Gravitational force acts downward on every object with mass. The heavier the athlete, the greater the gravitational pull. This force directly affects vertical movements like jumping and landing, as well as projectile motion when you throw or kick a ball.

Normal force is the support force a surface exerts on an object resting on it. When you stand on flat ground, the normal force pushes straight up, counteracting gravity. This force isn't constant during movement. During a landing, the normal force spikes well above your body weight. During the flight phase of a jump, it drops to zero because you've lost contact with the ground. These fluctuations are central to understanding balance and stability in ground-based sports.

Friction and Air Resistance

Friction opposes the relative motion between two surfaces in contact. It comes in two forms:

• Static friction prevents slipping. It's what keeps your foot planted when you push off during a sprint.
• Kinetic friction slows objects already in motion, like a sliding tackle on a soccer pitch.

Friction is vital for traction and grip in sports like sprinting, tennis, and rock climbing. Without enough friction, you can't generate the horizontal forces needed to accelerate or change direction.

Air resistance (drag) opposes motion through air and becomes increasingly significant at higher velocities. It affects both athletes moving at speed (cyclists, downhill skiers) and projectiles in flight (javelins, golf balls). Athletes and equipment designers actively work to minimize drag through aerodynamic postures, streamlined helmets, and skin-tight suits.

Lift and Elastic Forces

Lift force acts perpendicular to the direction of fluid flow. It's what makes a curveball curve: the spin of the ball creates a pressure difference on opposite sides, generating a sideways force. Lift is also critical in ski jumping (keeping the athlete airborne longer) and windsurfing.

Elastic forces store and release energy in deformable materials. A pole vaulter's pole bends and then snaps back, converting stored elastic energy into kinetic energy. The same principle applies to the strings of a tennis racket, the soles of running shoes, and plyometric exercises where tendons stretch and recoil. Training tools like resistance bands also rely on elastic force for rehabilitation and performance work.

Newton's Laws in Athletics

First Law of Motion: Inertia in Sports

Newton's First Law states that an object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by a net external force. This tendency to resist changes in motion is called inertia, and it's directly proportional to mass.

In sports, inertia explains why a heavier lineman is harder to move off the line of scrimmage, and why a lighter gymnast can change direction more quickly in the air. Athletes in contact sports like boxing or football use inertia to their advantage by bracing and maintaining posture during impacts. Coaches teach proper stance and body positioning partly based on inertia: a wider, lower stance increases stability because it takes more force to displace the athlete's center of mass.

Second Law of Motion: Force and Acceleration

Newton's Second Law quantifies the relationship between force, mass, and acceleration:

$F = ma$

This means the acceleration of an object equals the net force applied divided by its mass. A 60 kg sprinter who generates 600 N of horizontal force accelerates at 10 m/s², while a 100 kg sprinter needs to generate 1000 N to achieve the same acceleration.

This law is essential for analyzing power generation. It explains why strength training programs target both increasing force output and, in some cases, managing body mass. Explosive movements like jumping, throwing, and sprinting all depend on how much net force an athlete can produce relative to their mass.

Third Law of Motion: Action-Reaction in Sports

Newton's Third Law states that for every action force, there is an equal and opposite reaction force. These forces always act on different objects.

When a runner pushes backward against the ground (action), the ground pushes forward on the runner (reaction) with equal magnitude. When a swimmer pushes water backward, the water pushes the swimmer forward. In shot put, the athlete applies force to the shot, and the shot applies an equal force back on the athlete, which is why proper bracing and footwork matter so much.

In contact sports, this law governs collision forces. When two players collide, each experiences the same magnitude of force. Protective equipment like helmets and padding doesn't reduce the total force; it spreads it over a larger area and longer time to reduce injury risk.

Impulse and Momentum in Athletics

Impulse is derived from Newton's Second Law and equals force multiplied by the time over which it acts:

$J = F \times \Delta t$

Impulse equals the change in momentum ($p = mv$), so:

$F \times \Delta t = \Delta(mv)$

This relationship is why follow-through matters in striking sports. In golf or tennis, extending the contact time between the club/racket and ball increases the impulse delivered, producing a greater change in the ball's momentum.

The same principle works in reverse for safety. Protective equipment like crash mats, boxing gloves, and helmets increases the time over which an impact occurs. Spreading the same impulse over a longer time interval reduces the peak force, which is what actually causes injury. A gymnast bending their knees on landing uses the same strategy: increasing the deceleration time to lower the force on joints and bones.

Force, Mass, and Acceleration

Fundamental Relationship: F = ma

Newton's Second Law ($F = ma$) is the most frequently applied equation in sports biomechanics. Here, $F$ is the net force acting on the object, $m$ is mass, and $a$ is acceleration.

In practice, an athlete's strength-to-weight ratio often matters more than raw force production. A rock climber who weighs 55 kg and can pull with 600 N of force has a better strength-to-weight ratio than a 90 kg climber pulling with 800 N. This is why smaller athletes often excel in sports where you move your own body weight (gymnastics, climbing), while larger athletes dominate sports where you move external objects (shot put, lineman play).

Acceleration in Sports Context

Acceleration in sports isn't just about speeding up in a straight line. Any change in velocity counts, including slowing down (deceleration) and changing direction. A soccer player cutting left at full speed undergoes significant acceleration even if their speed barely changes, because the direction of their velocity changes.

The ability to accelerate depends on how quickly an athlete can generate force relative to their body mass. This is why training programs target both maximum force production and rate of force development (how fast you can reach peak force). Technologies like force plates and motion capture systems measure these variables precisely, giving coaches data to optimize training.

Power and Its Importance

Power combines force and velocity:

$P = F \times v$

Power tells you how quickly an athlete can do work. Two weightlifters might both deadlift 200 kg, but the one who lifts it faster produces more power. In explosive sports like sprinting, jumping, and Olympic lifting, power output is often a better predictor of performance than strength alone.

As with force, the power-to-weight ratio is frequently more relevant than absolute power. A cyclist producing 400 W who weighs 70 kg (5.7 W/kg) will climb faster than one producing 450 W at 90 kg (5.0 W/kg). Coaches use power metrics from force plates and velocity-based training devices to track athlete readiness and adjust training loads.

External Forces on Athletes

Gravity and Ground Reaction Forces

Gravity constantly pulls an athlete's center of mass downward, influencing balance, jump height, and the trajectory of airborne movement. You can't change gravity, but you can change how you interact with it.

Ground reaction forces (GRFs) are the forces the ground exerts back on an athlete in response to the forces the athlete applies (Newton's Third Law). Force plates measure GRFs in three directions: vertical, anterior-posterior (front-back), and medial-lateral (side-to-side). Analyzing GRF data reveals details about running mechanics, jump performance, and landing technique that aren't visible to the naked eye. For example, asymmetries in GRFs between left and right legs can signal injury risk before symptoms appear.

Air Resistance and Friction

At competitive speeds, air resistance becomes a major factor. A cyclist at 50 km/h spends roughly 90% of their energy overcoming drag. Strategies to minimize it include adopting aerodynamic tuck positions, drafting behind other competitors, and using streamlined equipment.

Friction between shoes (or equipment) and the playing surface determines how effectively an athlete can accelerate, decelerate, and change direction. Too little friction causes slipping; too much can increase the risk of knee injuries during sudden pivots. Sport-specific footwear is designed to optimize this balance for the demands of each surface and activity.

Rotational Forces and Contact Forces

Centripetal force is the inward-directed force required to keep an object moving in a circular path. A discus thrower spinning in the ring, a figure skater performing a spin, and a race car driver rounding a curve all depend on centripetal force. If this force is insufficient, the object or athlete moves outward along a tangent (which is what you feel as the outward "pull" often called centrifugal force, though it's technically not a real force but rather the effect of inertia).

In contact sports, external forces from opponents significantly affect motion and balance. Athletes in judo, rugby, and wrestling develop strategies to use an opponent's force against them or to maintain a stable base that resists displacement.

Force Analysis for Performance and Safety

Biomechanical force analysis serves two goals: improving performance and reducing injury risk. By measuring and modeling the forces acting on an athlete, coaches and sport scientists can:

• Identify inefficient movement patterns and correct technique flaws
• Design equipment that enhances performance (e.g., stiffer sprint spikes) or absorbs impact (e.g., improved helmet padding)
• Develop rehabilitation protocols that progressively reload injured tissues at safe force levels
• Inform rule changes and safety regulations to protect athletes from excessive or dangerous forces

This kind of analysis connects everything in this unit: Newton's laws, impulse-momentum relationships, and the interplay of internal and external forces all feed into practical decisions about how athletes train, compete, and recover.